One of the possible functions $f(x)$ which satisfies $\int_{-2}^{2} f(x) dx = 0$ is

Let $I = \int_{0}^{1} \frac{x^{3} \cos 3x}{2+x^{2}} dx$. Then

$\int_0^{\frac{\pi}{2}} \frac{\cos ^3 x}{\sin x+\cos x} d x=$

The option$(s)$ with the values of $a$ and $L$ that satisfy the following equation is(are) $\frac{\int_0^{4 \pi} e^t(\sin^6 at + \cos^4 at) dt}{\int_0^{\pi} e^t(\sin^6 at + \cos^4 at) dt} = L$.

If $\int_0^{10} f(x) d x=5$,then $\sum_{k=1}^{10} \int_0^1 f(k-1+x) d x=$

If $\int_0^\pi {x\,f({{\cos }^2}x + {{\tan }^4}x)\,dx} = k\int_0^{\pi /2} {f({{\cos }^2}x + {{\tan }^4}x)\,dx,}$ then the value of $k$ is